Basement Rough in Plumbing Identification and Solution

I'm planning to finish my basement and add a 3/4 bathroom. I'm not sure if I identified the rough ins properly. I attached the pictures and layout.

1. Toilet- I know that I identified the toilet rough in properly but i don't see any vents sticking out of the floor for the toilet. How do I solve the venting for this? Is there any digging involve.

2. Shower - Not sure if this pipe sticking out of the floor is for the shower. I hope it is. I'm planning to put a 36x60 shower pan here.

3. Vanity - For 40 inch vanity. Connect a vent pipe and connect it to the vent directly above it. See attached pic. May this can also serve as a vent for the shower. Not sure about the toilet because it's 7 feet from this rough in. See layout.

Let me know if I identified the rough ins properly and kindly advice on how to approach this layout to accomplish the above objectives. Your advice would be highly appreciated.

Are the red lines where you THINK the pipes are, or were you KNOW they because you saw them installed. It is NOT how I would have installed them, and without doing some checking, there is no way for use to tell you what the various pipes are for.

Are the red lines where you THINK the pipes are, or were you KNOW they because you saw them installed. It is NOT how I would have installed them, and without doing some checking, there is no way for use to tell you what the various pipes are for.

Click to expand...

The pipe in the square hole is the shower. The small one across from it is the drain / wet vent for the lav and shower and the big pipe is the toilet.

Thanks. The red lines are the distance between the opening of the rough ins shown in the pictures. I guess I have to jack hammer the slab to reposition the pipes to meet get the bathroom layout that I want.